A coaster brake would fine in cold and snow, many people I know really like them for winter riding.

Based on my experience with BSO's from the x marts of the world I do not think the hubs are going to hold up to any type of extreme riding and would certainly not want to try any technical riding with a coaster brake.

To get to this point I rode through the river and was crank deep in water... sealed hubs and a sealed bb are pretty much essential.